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A farmer collected data on the annual rainfall, x cm, and the annual yield of peas, p tonnes per acre - Edexcel - A-Level Maths Statistics - Question 4 - 2011 - Paper 1

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A farmer collected data on the annual rainfall, x cm, and the annual yield of peas, p tonnes per acre. The data for annual rainfall was coded using $v = \frac{x - 5... show full transcript

Worked Solution & Example Answer:A farmer collected data on the annual rainfall, x cm, and the annual yield of peas, p tonnes per acre - Edexcel - A-Level Maths Statistics - Question 4 - 2011 - Paper 1

Step 1

Find the equation of the regression line of p on v in the form $p = a + bv$

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Answer

To find the regression line, we first need to determine the slope (b) and the y-intercept (a).

The slope b is calculated using the formula: b=SpwSvb = \frac{S_{pw}}{S_v}

Substituting the values: b=1.1685.7530.203b = \frac{1.168}{5.753} \approx 0.203

Next, we calculate the intercept a using: a=pˉbvˉa = \bar{p} - b \bar{v}

Substituting in the known values: a=3.220.2034.423.220.8962.324a = 3.22 - 0.203 \cdot 4.42 \approx 3.22 - 0.896 \approx 2.324

Thus, the equation of the regression line is: p=2.324+0.203vp = 2.324 + 0.203v

Step 2

Using your regression line estimate the annual yield of peas per acre when the annual rainfall is 85 cm

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Answer

To estimate the yield when x=85x = 85 cm, we first compute the coded value v:

v=85510=8010=8v = \frac{85 - 5}{10} = \frac{80}{10} = 8

Next, substitute v into the regression equation: p=2.324+0.2038p = 2.324 + 0.203 \cdot 8

Calculating this gives: p=2.324+1.6243.948p = 2.324 + 1.624 \approx 3.948

Therefore, the estimated annual yield of peas per acre when the annual rainfall is 85 cm is approximately 3.95 tonnes.

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